You may be able to benefit from a device, such as nursery rhyme or song. If you practice reading the words, and if you can memorize some phrases, it gives you something that can be compared to a "machine". You just "turn it on" from your memory. This enables you to immediately pronounce a series of phrases from memory. As your use of "rhyming" sentences continues, you can feel more confidence about "blurting" out a few phrases and sentences.
Also, ordinary love songs, or "ballads" are an excellent study tool. to develop confidence in speaking. Because they are sung slowly, the words and phrases are very easy to follow.
Who knows? Maybe students of English could benefit from a Karaoke machine? But I will give you some examples of things that you can practice with. I will show you what I use with my language partners. You can find these on the Internet I think, without much difficulty.
"Ten Little Indians"
"This Old Man"
"There Was An Old Lady Who Swallowed A Fly"
"The House That Jack Built"
The Edgar Allen Poe poem, "Annabel Lee"
The song, "Turn, Turn, Turn" by The Byrds
The song, "You Send Me" by Sam Cooke
The song, "Wish You Were Here" by Pink Floyd
Finally, if you can get access to DVD's and a DVD player, start watching some of the great movie "musicals" and get a print out of their Lyrics (words of the song). Learn what the characters in the movie are singing. Learn the vocabulary. I will show you a list of Movie Musicals that are excellent for this kind of practice.